书图对圈的Ramsey数  

Ramsey Numbers of Books Versus Cycles

作　　者：方正 李双东 Fang Zheng;Li Shuangdong(School of Mathematical Sciences,Anhui University,Hefei 230601,China;Hefei Institute of Technology,Hefei 238076,China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601 [2]合肥理工学院,安徽合肥238076

出　　处：《南开大学学报（自然科学版）》2024年第5期111-114,共4页Journal of Nankai University(Natural Sience)

基　　金：国家自然科学基金(12071002);安徽省自然科学基金(2208085J22);安徽省教育厅基金(2023AH053262,2023AH050060)。

摘　　要：给定图G和H,其Ramsey数r(G,H)为最小的正整数N,使得对于完全图KN的任意红、蓝边着色,则总包含红色子图G或者蓝色子图H.给定正整数n和k,书图B_(n)(k)是由n个Kk+1共用一个Kk所构成的图.长度为m的圈记为C_(m).证明了当k≥3且n≥nk充分大时,r(B_(n)(k),C_(n))=(k+1)n-k,nk是一个依赖于k的常数.Let G and H be two given graphs.The Ramsey number r(G,H)is the least integer N such that for every graph F of order N,either F contains G or■contains H.Let B_(n)^((k))be the book graph which consists of n copies of K_(k+1)all sharing a common K_k,and let C_(m)be a cycle of length m.It's proved that when k≥3 and n≥n_(k),r(B_n~((k)),C_(n))=(k+1)n-k,where n_(k)is a constant dependent on k.

关 键 词：RAMSEY数 书图 圈 

分 类 号：O157.5[理学—数学]